“The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making.”

Morris Kline, p.22.
Mathematics for the Nonmathematician (1967)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematic…" by Morris Kline?

Morris Kline42

American mathematician 1908–1992

Related quotes

“It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 30 Reported in Memorabilia mathematica or, The philomath's quotation-book by Robert Edouard Moritz. Published 1914.

“Another feature of Alexandrian algebra is the absence of any explicit deductive structure. The various types of numbers… were not defined. Nor was there any axiomatic basis on which a deductive structure could be erected. The work of Heron, Nichomachus, and Diophantus, and of Archimedes as far as his arithmetic is concerned, reads like the procedural texts of the Egyptians and Babylonians… The deductive, orderly proof of Euclid and Apollonius, and of Archimedes' geometry is gone. The problems are inductive in spirit, in that they show methods for concrete problems that presumably apply to general classes whose extent is not specified. In view of the fact that as a consequence of the work of the classical Greeks mathematical results were supposed to be derived deductively from an explicit axiomatic basis, the emergence of an independent arithmetic and algebra with no logical structure of its own raised what became one of the great problems of the history of mathematics. This approach to arithmetic and algebra is the clearest indication of the Egyptian and Babylonian influences… Though the Alexandrian Greek algebraists did not seem to be concerned about this deficiency… it did trouble deeply the European mathematicians.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p.144

“The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.”

James Gow (scholar) (1854–1923) scholar

Preface
A Short History of Greek Mathematics (1884)

“The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the Arabs was what is commonly called rhetorical algebra. …on the whole they used ordinary rhetoric to describe their mathematical work. Symbolism is a relatively modern invention of the sixteenth and seventeenth centuries…”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 59

“It is true that in recent years a number of attractive histories of mathematics have been published in England and America, but these have only dealt with Greek mathematics as part of the larger subject, and in consequence the writers have been precluded… from presenting the work of the Greeks in suflicient detail. The same remark applies to the German histories of mathematics, even to the great work of Moritz Cantor…”

Thomas Little Heath (1861–1940) British civil servant and academic

Preface p. vi
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“Two thousand years of history Black History could not be wiped away so easily.”

Bob Marley (1945–1981) Jamaican singer, songwriter, musician

Zion Train
Uprising (1979)

“There is only one other survey, Datta and Singh’s 1938 History of Hindu Mathematics, recently reprinted but very hard to obtain in the West (I found a copy in a small specialized bookstore in Chennai). They describe in some detail the Indian work in arithmetic and algebra and, supplemented by the equally hard to find Geometry in Ancient and Medieval India by Sarasvati Amma (1979), one can get an overview of most topics.”

David Mumford (1937) American mathematician

[David Mumford, Book Review, Notices of the AMS, March 2010, 57, 3, http://www.ams.org/notices/201003/rtx100300385p.pdf]

“I think that the idea that a modern society would be able to establish itself as a multicultural society, with as many cultural groups as possible is absurd. One cannot make out of Germany with at least a thousand years of history since Otto I subsequently make a crucible.”

Helmut Schmidt (1918–2015) Chancellor of West Germany 1974-1982

Frankfurter Rundschau, 12. September 1992, S. 8, zitiert in konservativ.de http://www.konservativ.de/epoche/139/epo_139b.htm und linksnet.de http://www.linksnet.de/linkslog/index.php?itemid=431

“There is, for instance, only one page at the beginning of Runciman's three-volume History of the Crusades describing how the participants decided to begin four hundred years of wars, and then several thousand pages devoted to the routes, battles and other events which make up the "history" of the Crusades.”

Lloyd deMause (1931) American thinker

Source: Foundations of Psychohistory (1982), Ch. 2, p. 86.

“The moment we begin to map the history of money across the last five thousand years of Eurasian history, startling patterns begin to emerge.”

David Graeber (1961) American anthropologist and anarchist

Source: Debt: The First 5,000 Years (2011), Chapter Eight, "Credit versus Bullion", p. 212

“The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making.”

Help us to complete the source, original and additional information

Morris Kline42

Related quotes

Related topics